quadratic y cubic, quadrato-cuhic, and higher Surds, 35 
145V + 
+ 10015*/ 20025^f . + 3%"^- 
Arranged, 1-^76^: = +3432^'^^^ + ^oo^s'^t^.Ws't’^^oop^l'' ,W st'’ 
+ 10015''/*+ 3 ^ 4 ^^^ + 20025 ®/^. 
+- 145/* + /*. +"3^^^ * 
Restore, first, for s,±-^\/m : + ^ Vu ; for /, ± ^ 
then, 
— 4.5461m*. —1825m*. , 
•n — gogo 7 nn. \ nfl 42538m«. \U , 
iabc=.~ 
I / 2731m*. 
71 ^ -33+8m«. 
V+ 729 «*- 
m 
+ 364S«*. 
-~izgw‘. 
8 y 45461m*. 41825m*. 
k m. _J_ 4W. ^gogomn. + \/ m — 2538m«. \/ n . 
a -n. - y -n. +i 6 ^sn\ ~ +729’'*. 
Restore, secondly, for w, w — ; divide hy-^^\/c, and trans- 
pose : then. 
14m’ 
4 m*. 
— 
4 ^ 2 c^ i + f ± i Vm - 10 cm. X — - 4 . c 
- 3^6. +5^*- ^ ^7 
^ y w — 7“ 
4 i I i V , 
± i v'w 4 i ^ w — 4 + ^ 
45c*. 
4 ^ Vm — i ^ m — — 
+ Xv'm+”‘' 
• cm. X 2 V ''c _j_ locm. 2 
+ 
4 c*. 
±C 
27 
27 
6. 
Put, + i 3 ^ ^ 2x ; m* + loaii + c* = 2y ; 14774 
3 
+ SSC'w + 2c" — gab = gz : then, + x V m — y Vu . 
iL^V 7 n n + ±_xVui y \/n . — -j -v/zz 
+ z Wd = 0. 
Therefore, by the extermination of cubic surds, 
f xV in — y Vn . ±_ ^Vni Vn 
< -{• +xV ni y Vn^ , ±,^ Vm — \ Vn + = 3 . x"m — )7n 
L V m — ^ n . z^Vc^ = x^ni — y'^n . cz 
